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We study in this paper, a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper, the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piecewise affine function of the state and can be computed offline efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for an infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems. [ABSTRACT FROM AUTHOR]

This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $\Gamma _1 \subset \Gamma _2 \subset \mathbb {R}^n$ , with $\Gamma _1$ compact, the theorems presented in this paper give conditions under which a qualitative property of $\Gamma _1$ that holds relative to $\Gamma _2$ (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set $\Gamma _1$ , then $\Gamma _1$ is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed computation of the well-known linear matrix equation in the form of ${{AXB}} = F$ , with the matrices $A$ , $B$ , $X$ , and $F$ of appropriate dimensions, over multiagent networks from an optimization perspective. In this paper, we consider the standard distributed matrix-information structures, where each agent of the considered multiagent network has access to one of the subblock matrices of $A$ , $B$ , and $F$. To be specific, we first propose different decomposition methods to reformulate the matrix equations in standard structures as distributed constrained optimization problems by introducing substitutional variables; we show that the solutions of the reformulated distributed optimization problems are equivalent to least squares solutions to original matrix equations; and we design distributed continuous-time algorithms for the constrained optimization problems, even by using augmented matrices and a derivative feedback technique. Moreover, we prove the exponential convergence of the algorithms to a least squares solution to the matrix equation for any initial condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider the identification of matrix state-space models (MSSM) of the following form: \begin{align*} \mathbf {X}(k+1) &= \mathbf {A}_2 \mathbf {X}(k) \mathbf {A}_1^T + \mathbf {B}_2 \mathbf {U}(k) \mathbf {B}_1^T \\ \mathbf {Y}(k) &= \mathbf {C}_2 \mathbf {X}(k) \mathbf {C}_1^T + \mathbf {E}(k) \end{align*} for all time dependent quantities and matrices of appropriate dimensions. Due to the large size of these matrices, vectorization does not allow the use of standard multivariable subspace methods such as N4SID or MOESP. In this paper, the resulting Kronecker structure that appears in the system matrices due to vectorization is exploited for developing a scalable subspace-like identification approach. This approach consists of first estimating the Markov parameters associated to the MSSM via the solution of a regularized bilinear least-squares problem that is solved in a globally convergent manner. Second, a bilinear low-rank minimization problem is tackled which allows to write a three-dimensional low-rank tensor and consequently to estimate the state sequence and the lower-dimensional matrices $\mathbf {A}_1,\mathbf {A}_2,\mathbf {B}_1,\mathbf {B}_2,\mathbf {C}_1,\mathbf {C}_2$. A numerical example on a large-scale adaptive optics system demonstrates the ability of the algorithm to handle the identification of state-space models within the class of Kronecker structured matrices in a scalable manner which results in more compact models. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new state observer design technique for nonlinear systems. It combines the well-known Kazantzis–Kravaris–Luenberger observer and the recently introduced parameter estimation-based observer, which become special cases of it—extending the realm of applicability of both methods. A second contribution of this paper is the proof that these designs can be recast as particular cases of immersion and invariance observers—providing in this way a unified framework for their analysis and design. Simulation results of a physical system that illustrates the superior performance of the proposed observer compared to other existing observers are presented. [ABSTRACT FROM AUTHOR]

This work deals with the analysis and the design of minimum-time control laws for a class of nonlinear discrete-time dynamical systems characterized by \cal K-continuous transition maps and bounded control inputs. In the paper, it is shown that the reachability properties of the target set, even if not robust positively controllable in one state transition, can be exploited to assess the existence of a robust positively controllable set including the target in its interior. This result allows the formulation of a robustified minimum-time control policy, based on iterated online optimizations and guaranteeing the ultimate boundedness of the state-trajectories in the presence of bounded uncertainties, even if the target set is not robust positively controllable. [ABSTRACT FROM PUBLISHER]

This paper presents a numerical procedure for the reachability analysis of systems with nonlinear, semi-explicit, index-1 differential-algebraic equations. The procedure computes reachable sets for uncertain initial states and inputs in an overapproximative way, i.e. it is guaranteed that all possible trajectories of the system are enclosed. Thus, the result can be used for formal verification of system properties that can be specified in the state space as unsafe or goal regions. Due to the representation of reachable sets by zonotopes and the use of highly scalable operations on them, the presented approach scales favorably with the number of state variables. This makes it possible to solve problems of industry-relevant size, as demonstrated by a transient stability analysis of the IEEE 14-bus benchmark problem for power systems. [ABSTRACT FROM AUTHOR]

This paper considers the optimization problem for partially observable Markov decision processes (POMDPs) with the continuous state, observation, and action spaces. POMDPs with the discrete spaces have emerged as a promising approach to the decision systems with imperfect state information. However, in recent applications of POMDPs, there are many problems that have continuous states, observations, and actions. For such problems, due to the infinite dimensionality of the belief space, the existing studies usually discretize the continuous spaces with the sufficient or nonsufficient statistics, which may cause the curse of dimensionality and performance degradation. In this paper, based on the sensitivity analysis of the performance criteria, we have developed a simulation-based policy iteration algorithm to find the local optimal observation-based policy for POMDPs with the continuous spaces. The proposed algorithm needs none of the specific assumptions and prior information, and has a low computational complexity. One numerical example of the complicated multiple-input multiple-output beamforming problem shows that the algorithm has a significant performance improvement. [ABSTRACT FROM AUTHOR]

This paper proposes a new optimal control synthesis algorithm for multirobot systems under global temporal logic tasks. Existing planning approaches under global temporal goals rely on graph search techniques applied to a product automaton constructed among the robots. In this paper, we propose a new sampling-based algorithm that builds incrementally trees that approximate the state space and transitions of the synchronous product automaton. By approximating the product automaton by a tree rather than representing it explicitly, we require much fewer memory resources to store it and motion plans can be found by tracing sequences of parent nodes without the need for sophisticated graph search methods. This significantly increases the scalability of our algorithm compared to existing optimal control synthesis methods. We also show that the proposed algorithm is probabilistically complete and asymptotically optimal. Finally, we present numerical experiments showing that our approach can synthesize optimal plans from product automata with billions of states, which is not possible using standard optimal control synthesis algorithms or model checkers. [ABSTRACT FROM AUTHOR]

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the computational task, instead of using a single centralized processor to obtain a “global solution” of the scenario problem (SP), we resort to multiple interconnected processors that are distributed among different nodes of a network to simultaneously solve the SP. Then, we propose a primal-dual subgradient algorithm and a random projection algorithm to distributedly solve the SP over undirected and directed graphs, respectively. Both algorithms are given in an explicit recursive form with simple iterations, which are especially suited for processors with limited computational capability. We show that, if the underlying graph is strongly connected, each node asymptotically computes a common optimal solution to the SP with a convergence rate $O(1/(\sum _{t=1}^k\zeta ^t))$ , where $\lbrace \zeta ^t\rbrace$ is a sequence of appropriately decreasing stepsizes. That is, the RCO is effectively solved in a distributed way. The relations with the existing literature on robust convex programs are thoroughly discussed and an example of robust system identification is included to validate the effectiveness of our distributed algorithms. [ABSTRACT FROM AUTHOR]

The goal of this paper is to explore the relationship between the network graph of a state-space representation of an observed process and the causal relations among the components of that process. We will show that the existence of a linear time-invariant state-space representation, with its network graph being the star graph, is equivalent to (conditional) Granger noncausal relations among the components of the output process. Granger noncausality is a statistical concept, which applies to arbitrary processes and does not depend on the representation of the process. That is, we relate intrinsic properties of a process with the network graph of its state-space representations. [ABSTRACT FROM AUTHOR]

This paper will investigate the stabilization and optimal linear quadratic (LQ) control problems for infinite horizon discrete-time mean-field systems. Unlike the previous works, for the first time, the necessary and sufficient stabilization conditions are explored under mild conditions, and the optimal LQ controller for infinite horizon is designed with a coupled algebraic Riccati equation (ARE). More specifically, we show that under the exact detectability (exact observability) assumption, the mean-field system is stabilizable in the mean square sense with the optimal controller if and only if a coupled ARE has a unique positive semidefinite (positive definite) solution. The presented results are parallel to the classical results for the standard LQ control. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of computing the distance between a given singular descriptor system $ (E,A)$ , and a nearest descriptor system that has impulsive initial conditions. The link between existence of impulsive initial conditions and zeros at infinity for the associated matrix pencil $sE - A$ is well-known. Much of the literature focusses on the case when only one of $E$ and $A$ is perturbed. We give a closed form expression of the distance to a nearest descriptor system having impulsive solutions via rank-1 perturbations when both $E$ and $A$ are perturbed. Next, for the case of perturbations without rank restrictions, we propose and evaluate the bounds for the distance. In the context of structured perturbations, we formulate and obtain an explicit expression for the distance, when $E$ and $A$ are Hermitian and are perturbed by Hermitian matrices. For a suitable class of systems, we also show that upper and lower bounds are within a factor of $\sqrt{2}$. We finally construct examples and compare the bounds obtained from our results with those from the literature as well as with computed values of the distance obtained via three numerical optimization techniques such as the structured low rank approximation, the Broyden–Fletcher–Goldfarb–Shanno algorithm, and direct optimization tools like globalsearch. [ABSTRACT FROM AUTHOR]

The focal point of this paper is the well known problem of polynomial positivity over a given domain. More specifically, we consider a multivariate polynomial ƒ(x) with parameter vector x restricted to a hypercube X C Rn. The objective is to determine if ƒ(x) > 0 for all x E X. Motivated by NP-Hardness considerations, we introduce the so-called dilation integral method. Using this method, a "softening" of this problem is described. That is, rather than insisting that ƒ(x) be positive for all x ϵ X, we consider the notions of practical positivity and practical non-positivisy. As explained in the paper, these notions involve the calculation of a quantity e > 0 which serves as an upper bound on the percentage volume of violation in parameter space where ƒ(x) ≤ 0. Whereas checking the polynomial positivity requirement may be computationally prohibitive, using our ϵ-softening and associated dilation integrals, computations are typically straightforward. One highlight of this paper is that we obtain a sequence of upper bounds ϵk which are shown to be "sharp" in the sense that they converge to zero whenever the positivity requirement is satisfied. Since for fixed n, computational difficulties generally increase with k, this paper also focuses on results which reduce the size of the required k in order to achieve an acceptable percentage volume certification level. For large classes of problems, as the dimension of parameter space n grows, the required k value for acceptable percentage volume violation may be quite low. In fact, it is often the case that low volumes of violation can be achieved with values as low as k = 2. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust H∞ estimation for uncertain systems subject to limited communication capacity. The parameter uncertainty belongs to a given convex polytope and the communication limitations include measurement quantization, signal transmission delay, and data packet dropout, which appear typically in a network environment. The problem of H∞ filter design is first solved for a nominal system subject to the aforementioned information limitations, which is then extended to the uncertain case based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. The quadratic and parameter-dependent approaches provide alternatives for designing robust H∞ filters with different degrees of conservativeness and computational complexity. Two examples, including a mass-spring system, are utilized to illustrate the design procedures proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level. [ABSTRACT FROM AUTHOR]

This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state- and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed. [ABSTRACT FROM AUTHOR]

This paper deals with controllability of dynamical networks. It is often unfeasible or unnecessary to fully control large-scale networks, which motivates the control of a prescribed subset of agents of the network. This specific form of output control is known under the name target control. We consider target control of a family of linear control systems associated with a network, and provide both a necessary and a sufficient topological condition under which the network is strongly targeted controllable. Furthermore, a leader selection algorithm is presented to compute leader sets achieving target control. [ABSTRACT FROM PUBLISHER]

In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one. The second term is typically used to encode constraints or to regularize the solution. We propose a class of distributed optimization algorithms based on proximal gradient methods applied to the dual problem. We show that, by choosing suitable primal variable copies, the dual problem is itself separable when written in terms of conjugate functions, and the dual variables can be stacked into non-overlapping blocks associated to the computing nodes. We first show that a weighted proximal gradient on the dual function leads to a synchronous distributed algorithm with local dual proximal gradient updates at each node. Then, as main paper contribution, we develop asynchronous versions of the algorithm in which the node updates are triggered by local timers without any global iteration counter. The algorithms are shown to be proper randomized block-coordinate proximal gradient updates on the dual function. [ABSTRACT FROM PUBLISHER]

In this paper, stochastic systems with fractional Gaussian noise (fGn) are stochastically stabilized using a new robust sliding mode control scheme. The system is assumed to have state time delay and the system matrices have uncertainties. The proposed sliding hyper-surface is a fractional Ito process which is proven to be attainable almost surely in finite time by applying the fractional Ito formula. The trajectories of the system will be kept within a time-varying region around the sliding hyper-surface. The stochastic asymptotic stability of the closed-loop dynamics at sliding mode is guaranteed by the feasibility of some linear matrix inequalities (LMIs). The usefulness of the theoretical findings is demonstrated by providing a case study on the problem of stream water quality standards regulation. In addition, to show the effectiveness and superiority of the method a numerical example is presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generic notion of distance between systems that can be used to measure discrepancy between open-loop systems in a feedback sense under several uncertainty structures. When the uncertainty structure is chosen to be four-block (or equivalently, normalized coprime factor) uncertainty, then this generic distance measure reduces to the well-known v-gap metric. Associated with this generic distance notion, we also define a generic stability margin notion that allows us to give the distance measure a feedback interpretation by deriving generic robust stability and robust performance results. The proposed distance notion and the corresponding results exploit a powerful generalization of the small-gain theorem which handles perturbations in RL∞, rather than only in RH∞. When the uncertainty structure is fixed to one of the standard structures (e.g., additive, multiplicative, inverse multiplicative, coprime factor, four-block or any mixtures of the above), we give a step-by-step procedure (based on model validation ideas) that shows how the generic notion of distance and the correspondingly generic winding number conditions can be reduced to simple formulae. This work provides a unified framework that captures and embeds previous results in this area and also completes the picture by showing how other results of a similar nature can be obtained from the same framework. The techniques used involve only basic linear algebra, so they also provide a simplification of previous advanced proofs. Furthermore, the various distance measures so created can be used for non-conservative model embedding into the smallest uncertain family. An illustrative example is also given that demonstrates the superior qualities, above the v-gap metric, of a particular distance measure obtained from this work in situations where the plant is lightly-damped. All systems considered in this paper are linear time-invariant. [ABSTRACT FROM AUTHOR]

This paper addresses robust performance analysis problems of linear time-invariant (LTI) systems affected by real parametric uncertainties. These problems, known also as a special class of structured singular value computation problems, are inherently intractable (NP-hard problems). As such intensive research effort has been made to obtain computationally tractable and less conservative analysis conditions, when linear matrix inequality (LMI) plays an important. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything if the LMI at hand turns out to be infeasible. This motivates us to consider the dual of the LMI and examine the structure of the dual solution. By pursuing this direction, in this paper, we provide rank conditions on the dual solution matrix under which we can conclude that the underlying robust performance is never attained. In particular, a set of uncertain parameters that violates the specified performance can be computed. These results come from block-moment mate is structure of the dual variable, which is consistent with the recent results on polynomial optimization. This particular structure enables us to make good use of simultaneous diagonalizability property of commuting diagonalizable matrices so that the sound rank conditions fur the exactness verification can be obtained. [ABSTRACT FROM AUTHOR]

This paper proves that there are no zero-net wall-transpiration control strategies that can sustain net heat flux below the laminar level in an incompressible channel flow with constant-temperature walls. The result represents a fundamental limit on the performance of a controlled nonlinear system as measured by a linear cost function over a broad class of admissible initial conditions and control inputs, not a zero-sum tradeoff in the frequency domain or time domain. Both buoyancy effects (via the Boussinesq approximation) and viscous heating effects are accounted for, and phenomenological justification for the result is also given. The boundedness of solutions of the two-way coupled Navier—Stokes/energy equations (when both buoyancy and viscous heating are accounted for) is also discussed, and a new proof of existence under an appropriate small-data assumption is provided. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the relation between a recently proposed subspace method based on predictor identification (PBSID), known also as ‘whitening filter algorithm,’ and the classical CCA algorithm. The comparison is motivated by i) the fact that CCA is known to be asymptotically efficient for time series identification and optimal for white measured inputs and ii) some recent results showing that a number of recently developed algorithms are very closely related to PBSID. We show that PBSID is asymptotically equivalent to CCA precisely in the situations in which CCA is optimal while an ‘optimized’ version of PBSID behaves no worse than CCA also for nonwhite inputs. Even though PBSID (and its optimized version) are consistent regardless of the presence of feedback, in this paper we work under the assumption that there is no feedback to make the comparison with CCA meaningful. The results of this paper imply that the ‘optimized’ PBSID, besides being able to handle feedback, is to be preferred to CCA also when there is no feedback; only in very specific cases (white or no inputs) are the two algorithms (asymptotically) equivalent. [ABSTRACT FROM AUTHOR]

This paper considers nonsquare spectral factorization of nonlinear input affine state space systems in continuous time. More specifically, we obtain a parametrization of nonsquare spectral factors in terms of invariant Lagrangian submanifolds and associated solutions of Hamilton-Jacobi inequalities. This inequality is a nonlinear analogue of the bounded real lemma and the control algebraic Riccati inequality. By way of an application, we discuss an alternative characterization of minimum and maximum phase spectral factors and introduce the notion of a rigid nonlinear system. [ABSTRACT FROM AUTHOR]

This paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input-to-state stable inverse dynamics, subject to possibly unknown control direction. The contribution of the paper is two-fold. Firstly, we consider the problem of global regulation, instead of global asymptotic stabilization (GAS), for systems with generalized dynamic uncertainties. It is shown by an elementary example that GAS is not solvable using conventional smooth output feedback. Secondly, we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system. Using our framework, most of the known classes of output feedback form systems are broadened in several directions: unmeasured states and unknown parameters can appear nonlinearly, restrictive matching and growth assumptions are removed, the dynamic uncertainty satisfies the weaker condition of Sontag's integral input-to-state stability, and the sign of high-frequency gain may be unknown. A constructive strategy is proposed to design a dynamic output feedback control law, that drives the state to the origin while keeping all other closed-loop signals bounded. [ABSTRACT FROM AUTHOR]

This paper proposes distributed discrete-time algorithms to cooperatively solve an additive cost optimization problem in multiagent networks. The striking feature lies in the use of only the sign of relative state information between neighbors, which substantially differentiates our algorithms from others in the existing literature. We first interpret the proposed algorithms in terms of the penalty method in optimization theory and then perform nonasymptotic analysis to study convergence for static network graphs. Compared with the celebrated distributed subgradient algorithms, which, however, use the exact relative state information, the convergence speed is essentially not affected by the loss of information. We also study how introducing noise into the relative state information and randomly activated graphs affect the performance of our algorithms. Finally, we validate the theoretical results on a class of distributed quantile regression problems. [ABSTRACT FROM AUTHOR]

We are interested in understanding stability (almost sure boundedness) of stochastic approximation algorithms (SAs) driven by a “controlled Markov” process. Analyzing this class of algorithms is important, since many reinforcement learning (RL) algorithms can be cast as SAs driven by a “controlled Markov” process. In this paper, we present easily verifiable sufficient conditions for stability and convergence of SAs driven by a “controlled Markov” process. Many RL applications involve continuous state spaces. While our analysis readily ensures stability for such continuous state applications, traditional analyses do not. As compared to literature, our analysis presents a two-fold generalization: 1) the Markov process may evolve in a continuous state space and 2) the process need not be ergodic under any given stationary policy. Temporal difference (TD) learning is an important policy evaluation method in RL. The theory developed herein, is used to analyze generalized $\text{TD}(0)$ , an important variant of TD. Our theory is also used to analyze a TD formulation of supervised learning for forecasting problems. [ABSTRACT FROM AUTHOR]

Factor models are a very efficient way to describe high-dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in mathematical terms as follows. We are given the covariance matrix $\Sigma$ of the available data. $\Sigma$ must be additively decomposed as the sum of two positive semidefinite matrices $D$ and $L$ : $D$ —that accounts for the idiosyncratic noise affecting the knowledge of each component of the available vector of data—must be diagonal and $L$ must have the smallest possible rank in order to describe the available data in terms of the smallest possible number of independent factors. In practice, however, the matrix $\Sigma$ is typically unknown and therefore it must be estimated from the data so that only an approximation of $\Sigma$ is actually available. This paper discusses the issues that arise from this uncertainty and provides a strategy to deal with the problem of robustly estimating the number of factors. [ABSTRACT FROM AUTHOR]

It is proved in this paper that the existence of suitable multiple Lyapunov functions is a necessary and sufficient condition for a discrete-time nonlinear switching system, with given switches digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the switches digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the first passage discounted payoff criterion for continuous-time $N$ -person nonzero-sum stochastic games in countable states and Borel action spaces, where the discount factor is nonconstant. For the game with unbounded reward functions and transition rates, the optimality is over the set of all randomized history-dependent policies. After showing the uniqueness of the solution to the Shapley equation, we give some suitable conditions imposed on the primitive data for the existence of Nash equilibria. Then, a financial system is introduced to illustrate the applications of the main result here. [ABSTRACT FROM AUTHOR]

This paper considers a class of stochastic source-seeking problems to drive a mobile robot to the minimizer of a source signal. Our approach is first analyzed in an obstacle-free scenario, where measurements of the signal at the robot location and information of a contact sensor are required. We extend our results to environments with obstacles under mild assumptions on the step size. Our approach builds on the simultaneous perturbation stochastic approximation idea to obtain information of the signal field. We prove the practical convergence of the algorithms to a ball whose size depends on the step size that contains the location of the source. The novelty relies in that we consider nondifferentiable convex functions, a fixed step size, and the environment may contain obstacles. Our proof methods employ nonsmooth Lyapunov function theory, tools from convex analysis, and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithms in a two-dimensional scenarios. [ABSTRACT FROM AUTHOR]

This paper presents continuous-time multiagent systems for distributed minimax optimization subject to bounded constraints. All agents in the system are divided into two groups for minimization and maximization. The multiagent system features competitive intergroup interactions and cooperative intragroup interactions, both of which are based on the output information of agents. First, a proportional-integral (PI) intragroup interaction rule is utilized for consensus within each group in the system. With this interaction rule, the system is proved to be convergent to an optimal solution to the problem, under a certain requirement on the intergroup interactions. Second, another discontinuous intragroup interaction rule is introduced. It is proved that the system with such an interaction is still convergent to an optimal solution if the proportional gain exceeds a derived lower bound, without the previous requirement on the intergroup interactions. As a special case, the systems are further applied for distributed optimization. Finally, simulation results are presented to substantiate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global exponential stability of a $2\times 2$ linear hyperbolic system with a sampled-data boundary feedback control designed by means of the backstepping method for a nominal continuous input. We show that there exists a sufficiently small intersampling time (that encompasses both periodic and aperiodic sampling) for which the global exponential stability of the closed-loop system is guaranteed. In addition, we provide easily tractable sufficient stability conditions that can be used to find an upper bound of the maximum intersampling time. The results rely on the combination of the Lyapunov method and looped-functionals. The effectiveness of the proposed results is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

This paper deals with the consensus tracking problem for a multiagent system with nonholonomic chained-form dynamics. A new distributed observer is first proposed for each follower to estimate the leader state and the leader input in a prescribed finite-time under both undirected and directed communication graphs. Then based on the observer and by adding a power integrator, a novel nonlinear protocol is designed such that the estimated leader state is tracked in a prescribed finite-time. Different from some existing finite-time consensus tracking approaches, an explicit bound without dependence on initial states is derived for the settling time. Therefore, in an unknown environment where initial conditions are unavailable, the proposed strategy is able to meet specific system requirements, e.g., a military target is tracked by a group of field robots in a prescribed time. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

In this paper, a new approach based on convex analysis is introduced to solve the $H_\infty$ problem for discrete-time nonlinear stochastic systems. First, by using the disintegration property of the conditional expectation, sufficient/necessary conditions are given for the internal stability of the concerned systems. Second, in order to separate the unknown exogenous disturbance from the state variables, the properties of convex functions are applied to prove the stochastic version of bounded real lemma (BRL). Third, the state feedback $H_\infty$ control problem is studied, and an $H_\infty$ control is designed based on the BRL. Finally, two numerical examples and one real-world regulation control example of synthetic genetic circuit are presented to show the effectiveness of our developed theory. [ABSTRACT FROM AUTHOR]

Equilibrium-independent dissipativity (EID) is a recently introduced system property that requires a system to be dissipative with respect to any forced equilibrium configuration. This paper is a detailed examination of EID with quadratic supply rates for a common class of nonlinear control-affine systems. We provide an algebraic characterization of EID for such systems in the spirit of the Hill–Moylan lemma, where the usual stability condition is replaced by an incremental stability condition. Based on this characterization, we state results concerning internal stability, feedback stability, and absolute stability of EID systems. Finally, we study EID for discrete-time systems, providing the relevant definitions and an analogous Hill–Moylan-type characterization. Results for both continuous-time and discrete-time systems are illustrated through examples on physical systems and convex optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper considers the problem of a leader that seeks to optimally influence the opinions of agents in a directed network through connecting with a limited number of the agents (“direct followers”), possibly in the presence of a fixed competing leader. The settings involving a single leader and two competing leaders are unified into a general combinatoric optimization problem, for which two heuristic approaches are developed. The first approach is based on a convex relaxation scheme, possibly in combination with the $\ell _1$ -norm regularization technique, and the second is based on a greedy selection strategy. The main technical novelties of this work are in the establishment of supermodularity of the objective function and convexity of its continuous relaxation. The greedy approach is guaranteed to have a lower bound on the approximation ratio sharper than $(1-1/e)$ , while the convex approach can benefit from efficient (customized) numerical solvers to have practically comparable solutions possibly with faster computation times. The two approaches can be combined to provide improved results. In numerical examples, the approximation ratio can be made to reach ${\text{90}\%}$ or higher depending on the number of direct followers. [ABSTRACT FROM AUTHOR]

This paper considers the stability analysis of nonlinear Lurie type systems where the nonlinearity is both (locally) sector and slope restricted. Convex conditions for verifying stability, computing outer estimates of reachable sets, and upper bounds on the induced $\mathcal {L}_2$ gain in a local or global domain are proposed. The conditions use a Lyapunov function that is quadratic on both the states and the nonlinearity and has an integral term on the nonlinearity. Numerical examples outline the benefits of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a detection algorithm for sensor attacks and a resilient state estimation scheme for a class of uniformly observable nonlinear systems. An adversary is supposed to corrupt a subset of sensors with the possibly unbounded signals, while the system has sensor redundancy. We design an individual high-gain observer for each measurement output so that only the observable portion of the system state is obtained. Then, a nonlinear error correcting problem is solved by collecting all the information from those partial observers and exploiting redundancy. A computationally efficient, on-line monitoring scheme is presented for attack detection. Based on the attack detection scheme, an algorithm for resilient state estimation is provided. The simulation results demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Networked control systems (NCSs) are distributed systems where plants, sensors, actuators, and controllers communicate over shared networks. Nonideal behaviors of the communication network include variable sampling/transmission intervals and communication delays, packet losses, communication constraints, and quantization errors. NCSs have been the object of intensive study in the last few years. However, due to the inherent complexity of NCSs, the current literature focuses on a subset of these nonidealities and mostly considers stability and stabilizability problems. Recent technology advances need different and more complex control objectives to be considered. In this paper, we present first a general model of NCS, including most relevant nonidealities of the communication network; then, we propose a symbolic model approach to the control design with objectives expressed in terms of nondeterministic transition systems. The presented results are based on recent advances in symbolic control design of continuous and hybrid systems. An example in the context of robot motion planning with remote control is included, showing the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information on the others’ decisions. We start from a continuous-time gradient-play dynamics that converges to an NE under strict monotonicity of the pseudogradient and assumes perfect information. We consider how to modify it in the case of partial, or networked information between players. We propose an augmented gradient-play dynamics with correction, in which players communicate locally only with their neighbors to compute an estimate of the other players’ actions. We derive the new dynamics based on the reformulation as a multiagent coordination problem over an undirected graph. We exploit incremental passivity properties and show that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbors. Under a strict monotonicity property of the pseudogradient, we show that the augmented gradient-play dynamics converges to consensus on the NE of the game. We further discuss two cases that highlight the tradeoff between properties of the game and the communication graph. [ABSTRACT FROM AUTHOR]

In this paper, we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear-nonquadratic performance functional for Filippov dynamical systems. Specifically, we consider dynamical systems with Lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving Filippov set-valued maps. In addition, we extend classical dissipativity theory to address the problem of dissipative discontinuous dynamical systems. These results are then used to derive extended Kalman-Yakubovich-Popov conditions for characterizing necessary and sufficient conditions for dissipativity of discontinuous systems using Clarke gradients and locally Lipschitz continuous storage functions. Furthermore, using the newly developed dissipativity notions we develop a return difference inequality to provide connections between dissipativity and optimality of nonlinear discontinuous controllers for Filippov dynamical systems. Specifically, using the extended Kalman-Yakubovich-Popov conditions we show that our discontinuous feedback control law satisfies a return difference inequality if and only if the controller is dissipative with respect to a quadratic supply rate. [ABSTRACT FROM AUTHOR]

The article presents abstracts of mathematical studies. They include "Approximation Metrics Discrete and Continuous Systems," "Stabilization of Planar Collective Motion: All-to-All Communication," and "Time-Varying Linear Systems: Relative Degree and Normal Form."

The state estimation for linear discrete-time systems with non-Gaussian state and output noise is a challenging problem. In this paper, we derive the suboptimal quadratic estimate of the state by means of a recursive algorithm. The solution is obtained by applying the Kalman filter to a suitably augmented system, which is fully observable. The augmented system is constructed as the aggregate of the actual system, and the observable part of a system having as state the second Kronecker power of the original state, namely the quadratic system. To extract the observable part of the quadratic system, the rank of the corresponding observability matrix is needed, which is a difficult task. We provide a closed form expression for such a rank, as a function of the spectrum of the dynamical matrix of the original system. This approach guarantees the internal stability of the estimation filter, and moreover, permits a reduction in the computational burden. [ABSTRACT FROM PUBLISHER]

In this paper, we first establish a stability result for a class of linear switched systems involving Kronecker product. The problem is interesting in that the system matrix does not have to be Hurwitz at any time instant. This class of linear switched systems arises in the control of multi-agent systems under switching network topology. As applications of this stability result, we give the solvability conditions for both the leaderless consensus problem and the leader-following consensus problem for general marginally stable linear multi-agent systems under switching network topology. In contrast with some existing results, our results only assume that the dynamic graph is uniformly connected. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of robust experiment design, i.e., how to design an input signal which gives relatively good estimation performance over a large number of systems and model structures. Specifically, we formulate the robust experiment design problem utilizing fundamental limitations on the variance of estimated parametric models as constraints. Using this formulation we design an input signal for situations where only diffuse a priori information is known about the system. Furthermore, we present a robust version of the unprejudiced optimal input design problem. To achieve this, we first develop a closed form solution for the input spectrum which minimizes the maximum weighted integral of the variance of the frequency response estimate over all model structures. [ABSTRACT FROM PUBLISHER]

A quite comprehensive theory of analytic interpolation with degree constraint, dealing with rational analytic interpolants with an a priori bound, has been developed in recent years. In this paper, we consider the limit case when this bound is removed, and only stable interpolants with a prescribed maximum degree are sought. This leads to weighted H[sub2] minimization, where the interpolants are parameterized by the weights. The inverse problem of determining the weight given a desired interpolant profile is considered, and a rational approximation procedure based on the theory is proposed. This provides a tool for tuning the solution to specifications. The basic idea could also be applied to the case with bounded analytic interpolants. [ABSTRACT FROM AUTHOR]

This paper deals with the state estimation problem for stochastic nonlinear differential systems, driven by standard Wiener processes, and presents a filter that is a generalization of the classical Extended Kalman-Bucy filter (EKBF). While the EKBF is designed on the basis of a first order approximation of the system around the current estimate, the proposed filter exploits a Carleman-like approximation of a chosen degree v ≥ 1. The approximation procedure, applied to both the state and the measurement equations, allows to define an approximate representation of the system by means of a bilinear system, for which a filtering algorithm is available from the literature. Numerical simulations on an example show the improvement, in terms of sample error covariance, of the filter based on the first-order, second-order and third-order system approximations (v = 1,2,3). [ABSTRACT FROM AUTHOR]